Last week, I made a surprising discovery about Facebook: It has far fewer “active” users than it claims. I learned this from a note buried deep in the company’s S1 — the IPO document it filed with the SEC in order to go public. Based on its S1, the social-networking giant’s value is probably much less than most investors seem to think.

One advantage of working in finance is that you get to meet lots of very nice, really smart people such as David Wilson, who writes the Chart of the Day column for Bloomberg. His column is my Sudoku, as I challenge myself to poke holes in the correlations it identifies between various assets. It’s good wonky fun.

On Feb. 3, the column used Facebook’s SEC data to show how fast the firm was growing. FB was becoming a “daily habit for more users,” and the numbers from the IPO filing were extraordinary: 845 million Monthly Active Users and 483 million Daily Active Users.

MAU? DAU? I had never heard of either metric, and novel accounting for public companies is always a red flag. Don’t just take my word for it, ask a Groupon investor.

I thought these metrics were suspect. If you do not have to go to Facebook.com to be counted as an active user, are the metrics misleading? I asked Wilson, who pointed to details in the S1:

“Daily Active Users (DAUs). We define a daily active user as a registered Facebook user who logged in and visited Facebook through our Web site or a mobile device, or took an action to share content or activity with his or her Facebook friends or connections via a third-party Web site that is integrated with Facebook, on a given day. We view DAUs, and DAUs as a percentage of MAUs, as measures of user engagement.”

Let me translate: If you clicked a “Like” button anywhere on the Internet, then you are a Daily Active User. Even if you never go to Facebook.com.

As huge as those MAU/DAU numbers were, I wondered how this detail might affect revenue. The Facebook metrics for annual revenue per user were stunningly modest: Facebook picks up $5 per user each year. Compare that to Google, which garners more than $30 per user per year. Netflix takes in closer to $144. Is this why Facebook’s annual revenues are so low compared to its 850 million user base?

Why does this user-behavior metric matter? Consider what it means in terms of how “daily users” will generate revenue and profits. If all users do is click a “Like” button, but never make it to Facebook.com, they cannot be “monetized.” They cannot be marketed to. They do not see any advertising. They cannot be sold any goods or services. They take advantage of FB’s extensive infrastructure to tell their FB friends (who may or may not see what they did) that they liked something online. That’s all that happens.

So they not only fail to generate revenue for Facebook that day, but they are actually a cost. It’s not cheap to maintain that massive infrastructure of Like buttons everywhere. Someone’s got to pay for the server farms that handle the back-end of this.

Consider what happened when MySpace tried to increase profits from users. With lots of pressure to drive revenue, they doubled the ads on the site. As they tried to monetize users, the site became ad-congested, a real eyesore. Users left in droves.

So how does this play into Facebook’s sky-high valuation? The company’s worth has been pushed ever higher by a series of private deals, all made before the SEC filing was made public. Microsoft made a well-timed investment of $240 million in 2008 at a $15 billion level; Elevation Partners paid $120 million at a value of $23 billion in June 2010. Goldman Sachs poured up to $2 billion into the social network at a $50 billion valuation in January 2011. All of these private investments were made by sophisticated investors, but without the benefit of the SEC data.

A year ago, I offered five questions for Facebook private investors:

●FB claimed (in January 2011) 500 million subscribers. How many of these are active users — at least once or twice a week? How many of these are dead accounts, with no activity for 30 days, 90 days or more?

●What is the average revenue per subscriber? How are you planning to grow this?

● How much churn does Facebook go through? For every 100 new subscribers, how many subscribers leave?

●What is the life cycle of the typical Facebook subscriber? How active are they for how long; what sort of arc do they cut across their FB life cycle?

●Besides advertising, how will you monetize your user base? Are you selling their data to buyers? What about anonymized data — are you selling this also?

Last month, I compiled a new list for Facebook IPO investors. Those of you thinking of buying Facebook’s IPO at these rich valuations should be comfortable with the answers to these:

●What is the IPO offering price going to be? What market capitalization will FB come public at?

●What is FB’s growth potential? At 800 million users, where do they begin to plateau? Top out?

●What is FB’s plan for penetrating China?

●How are the privacy concerns going to be handled? What else might come out of the closer FTC scrutiny of Web firms’ use of personal data?

●How long are insiders/VCs going to be locked up? Are they committed to holding onto shares for the long haul, or are they cashing out at the IPO or as soon as possible thereafter?

What I learned from Facebook’s filing was that they have 161 million active users who actually go to Facebook.com each month. That’s not shabby — but it’s a far cry from the MAU claims of 850 million. That definition of active users is probably overstated by a factor of 500 percent. I suspect that the $100 billion valuation may be overstated by nearly as much.

Me? I’m sitting this one out.

Ritholtz is chief executive of FusionIQ, a quantitative research firm. He is the author of “Bailout Nation” and runs a finance blog, the Big Picture.

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